I had no rat trouble until the big black snakes that used to live under and around my coops disappeared.
Then the rats moved in. I fought them with traps for many months which was a losing battle.
I finally resorted to using a low risk of secondary poisoning rat bait...Just One Bite. I bought 6 locking bait stations and placed them throughout my pens. Within a week there was much less rat activity and after 2 weeks I saw none. I wish I had used it many months before I did, but I have many barn cats and also outside dogs that I was scared of poisoning them . The vets I talked to before using it said they'd have to eat many dead rats within a short time frame to be affected. I lost no cats or dogs because of the dead rats.
Most of the rats died down in their tunnels and the ones that did die about ground the chickens ignored.
I now keep the baited stations out all the time and never see any sign of rats.
And yes, they will take and kill birds.